The 12th seed, who had lost three of his four tiebreaks in the two weeks leading into the event, put an end to the tense battle when he fired down an ace on his third match point to set up a clash with Chilean Cristian Garin.
Canadian teenager Felix Auger-Aliassime also secured a spot in the second round of the US Open tune-up with a 6-2 6-7(3) 7-6(3) win over compatriot Vasek Pospisil.
Awaiting 18-year-old Auger-Aliassime is 17th-seeded fellow Canadian Milos Raonic, who crushed 16 aces en route to a 6-4 6-4 win over Frenchman Lucas Pouille.
British qualifier Dan Evans faces a tough second-round clash against top seed and defending champion Rafa Nadal after beating Australian Alex de Minaur 6-4 7-6(6).
Croatia's Marin Cilic, the 14th seed, got past American qualifier Bradley Klahn 6-3 7-6(7) to advance, while Argentine Guido Pella upset Belgian 15th seed David Goffin 6-4 7-6(4).
2014 champion Jo-Wilfried Tsonga lost 6-2 6-2 to German Jan-Lennard Struff, while 16th seed Gael Monfils survived a scare from world No. 172 Peter Polansky before advancing 6-7(4) 6-3 6-3.
Monfils will next meet qualifier Ilya Ivashka, who was a straight-sets winner over South Korea's Kwon Soon-woo.
Three-time Grand Slam champion Stan Wawrinka, 10th seed Roberto Bautista Agut and American Tommy Paul were among the other players to advance to the second round.
On the women’s side, world number one Ash Barty's US Open tune-up got off to a rocky start as the Australian suffered a shock 6-7(5) 6-3 6-4 loss to American Sofia Kenin in the second round on Tuesday.
In earlier action, seven-times Grand Slam champion Venus Williams was eliminated in the first round after suffering a 6-4 6-2 loss to Spaniard Carla Suarez-Navarro, who will next face Estonian 16th seed Annett Kontaveit.
